# Arithmetic of curves on moduli of local systems

@article{Whang2018ArithmeticOC, title={Arithmetic of curves on moduli of local systems}, author={Junho Peter Whang}, journal={arXiv: Number Theory}, year={2018} }

We study the Diophantine geometry of algebraic curves on relative moduli of special linear rank two local systems over surfaces. We prove that the set of integral points on any nondegenerately embedded algebraic curve can be effectively determined. Under natural hypotheses on the embedding in relation to mapping class group dynamics of the moduli space, the set of all imaginary quadratic integral points on the curve is shown to be finite. Our ingredients include a boundedness result for…

## 4 Citations

Diophantine Analysis on Moduli of Local Systems

- Mathematics
- 2018

We develop a Diophantine analysis on moduli of special linear rank two local systems over surfaces with prescribed boundary traces. We first show that such a moduli space is a log Calabi-Yau variety…

Global geometry on moduli of local systems for surfaces with boundary

- MathematicsCompositio Mathematica
- 2020

Abstract We show that every coarse moduli space, parametrizing complex special linear rank-2 local systems with fixed boundary traces on a surface with nonempty boundary, is log Calabi–Yau in that it…

Nonlinear descent on moduli of local systems

- Mathematics
- 2017

We establish a structure theorem for the integral points on moduli of special linear rank two local systems over surfaces, using mapping class group descent and boundedness results for systoles of…

Surfaces, braids, Stokes matrices, and points on spheres

- Mathematics
- 2020

Moduli spaces of points on $n$-spheres carry natural actions of braid groups. For $n=0$, $1$, and $3$, we prove that these symmetries extend to actions of mapping class groups of positive genus…

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Abstract We show that every coarse moduli space, parametrizing complex special linear rank-2 local systems with fixed boundary traces on a surface with nonempty boundary, is log Calabi–Yau in that it…

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